The incident happened around 10.10am today at Myrehead Farm, which lies just off the A803, between Linlithgow and Falkirk.
The men sustained serious injuries and were pronounced dead at the scene.
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Two other men were also injured as a result of the collapse.
One was taken by ambulance to the Edinburgh Royal Infirmary, while the other was airlifted to the Queen Elizabeth University Hospital in Glasgow.
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Police say that at this time it is not believed they have sustained life-threatening injuries.
Inquiries to establish the full circumstances are ongoing and the Health and Safety Executive have been informed.
Chief Inspector Damian Armstrong, Local Area Commander for Falkirk said: “My thoughts and sympathies are with the families of those affected by this incident and a multi-agency inquiry at the farm is ongoing.
“If anyone believes they have any relevant information that may be of use to this investigation then please come forward and quote incident 1081 of May 6.”